The measured results are shown below with an order of a LC cell with strong mechanical rubbing, a photoalignment cell with photoactive polyimide RN1349 (from
Nissan Chemical Ltd.), and a photoalignment cell with composite layers of RN1349
and LCP (liquid crystal polymer). The results were taken at one specific position on each cell.
10-6 10-5 10-4 10-3 10-2 10-1 100 solid lines are their corresponding fitting results. The fitting model is the stretched exponential function g(2)( )t = +A Bexp⎡⎣−(t τ)s⎤⎦ . τ is the correlation time and s is the stretching parameter.
The discussion in section 2.3 led us to choose a stretched exponential function as the fitting model for the relaxation dynamics of LC’s molecular fluctuations in a cell. The fitting parameter τ represents the correlation time of the relaxation dynamics; the fitting parameter s can be used as a measure to reveal how close the dynamics approaches a single fluctuation mode. If the fluctuating dynamics is exactly a single fluctuation mode without any mode-mixing, s shall be equal to unity.
As shown in Fig. 2-4-3, the fitting parameters are τ =0.5403 ms and
s = for the photoalignment cell with composite layers of RN1349 and LCP.
From these fitting data, we can easily observe the differences among them. Firstly, the correlation time for the strong mechanical rubbing cell is less than those for the photoalignment cells by about one order of magnitude. Secondly, as to the photoalignment cells, the value taken by s seems to depend on whether LCP was deposited on RN1349 layer or not. Let us examine these two major differences with more caution.
We begin the discussion by examining the difference of the correlation time. In section 2.3, we achieved a conclusion that the correlation time is highly correlated with the surface anchoring energy coefficient. This hints that the difference of the correlation time may come from the difference in surface anchoring strengths of LC cells.
Having derived the τ−W relationships in section 2.3, we can use these relationships to determine the anchoring energy coefficient W of each cell.
According to many reports published in literature, surface rubbing treatment usually generates rather strong surface anchoring strength, whereas the UV-induced alignment shows weak anchoring strength. We therefore expect that our strong mechanical rubbing cell is strong anchoring and our photoalignment cells are weak anchoring. We then retrieve the corresponding anchoring energy coefficients from the measured data to see whether these retrieved values are in accord with the expected results.
From Eq. (2.3.2)
by substituting all the parameters of the rubbing cell with known values into the equation
W × − J m . Here, the effective Frank elastic constant
( )
1 10 11
K × − N and the rotational viscosity η 50 mPa s
(
⋅)
at T =25 °C [25].For the photoalignment cells, we adopt the following approximative formula for
Similarly, by substituting all the parameters of the photoalignment cells with known
values into Eq. (2.3.3), it yields 3 6 6 3
Having derived all the three cells’ anchoring energy coefficients, let us check these results to see whether they are reasonable or not. We expected high anchoring strength from the strong mechanical rubbing cell and our measured anchoring
coefficient is Wrubbing 6.014 10× −4
(
J m2)
. We expected that the photoalignment cells are weak anchoring and our measured values are: Wphoto. 8.093 10× −6(
J m2)
and Wphoto.+LCP 7.945 10× −6
(
J m2)
. The results agree well with our expectation, and thus we confidently conclude that the mechanically rubbing-induced anchoringstrength is much larger than that from photoalignment mechanism by about two orders of magnitude.
Let us examine the schematic shown below to intuitively illustrate the inverse tendency between τ and W.
(1)
n n
( )
τAs shown in the figure, photocounts n
( )
τ at a delay τ will be very close to the initial photocounts (1)n , provided that the delay τ is very small. This is because what the incident light field sees are the almost identical geometric configurations due to the“collective＂excitation nature of LC. In other words, after the delay τ , the collective excitation of LC molecules just produces a small rotation, the incident light field shall therefore see very similar geometric configuration except for the LC molecule marked by blue color shown in Fig. 2-4-4. Seeing a similar geometric configuration implies that the transmitted light fields will be also very alike.Therefore, n
( )
τ must be very close to n(1) , and this is the origin of the Fig. 2-4-4 The self-similarity existing in the collective excitation of LC Goldstone mode: Yellow wave represents the incident light field. (1)n is the photoelectron pulses counted at initial time, and( )
n τ is the photocounts at a delay τ from the initial time.
self-similarity in photocounts. Once the self-similarity is confirmed, the principle of the Schwartz’s inequality discussed in subsection 1.3.1 assures a high correlation value.
How about the decay behavior? The explanation could also be found with this picture. As the delay time τ becomes larger, the collective excitation of LC molecules generates a much larger rotation. At this stage, the incident light field experiences a configuration less similar to that in the initial time. This leads to a smaller degree of similarity between n(1) and n
( )
τ and a lower correlation value.The larger the delay time τ is, the smaller the correlation value will be.
We can extend these intuitive pictures to yield a connection with the LC cell’s surface anchoring strength. We have understood that the high correlation values result from the similar configurations the incident light field experiences. As time goes by, the transient LC configuration is less and less similar to the initial one. But how fast does the LC configuration changes from the most similar one to the least similar one?
To answer this question, we need a reference to compare with! Since the excitations in LC cells are collective, the effective wavelength λE of the standing wave induced by the collective excitation in a confined cell can be used to reveal the changing rate of LC configuration. When λE is large, the LC spends more time to change from the most similar configuration to the least similar one. Whereas when λE is small, it
takes the LC configuration less time to evolve. The comparison must be taken under the same physical conditions, that is, the same viscosity, the same ambient temperature, etc.
Let us consider two limiting cases: infinitely strong anchoring cell and weak anchoring cell. In the infinitely strong anchoring cell, the two substrates anchor the contacting LC molecules tightly, so these two contact surfaces play roles as nodal points of the standing wave. The effective λE is thus equal to the cell gap d. In the weak anchoring cell, the two substrates anchor the contacting LC molecules loosely, the effective λE could be lager than the cell gap d. Since we have shown that for longer λE LC medium spends more time on evolving their configuration. This leads to that a weak anchoring cell will spend more time to change its molecular configuration. The concept of the“more time” implies“larger correlation time＂
because it is this time that reflects correctly the rate of LC configuration changing from high to low correlation. Hence, we reach the point that a weak anchoring cell exhibits a characteristic long correlation time in its scattered optical signal; Similar analysis on an infinitely strong anchoring cell reveals that a strong anchoring cell shall possess a small correlation time in its scattered optical signal. Two illustrating schematic diagrams are shown below to facilitate our interpretation.
λE
d
λE
( )
a( )
bUp to now, we have only examined the difference in correlation time among cells with different surface treatment. Next we shall study the difference in the stretching parameters. In the beginning, we have mentioned that s can be used as a measure of how close the fluctuation approaches a purely single exponential dynamics. The s obtained from the two photoalignment cells are different. It appears that the cell with LCP has a purer fluctuation dynamics than that one without LCP. We are interested to know about what role LCP plays in the photoaligning process.
A LCP is a polymer produced by binding mesogenic molecules together. In our experiment, the LCP we used was 1,4-phenylene-bis{4-[6-(acryloyloxy)-hexyloxy]
benzoate}, whose structural formula is depicted in Fig. 2-4-6 (a) below.
Fig. 2-4-5 (a) Effective λE of the collective excitation-induced standing wave in the strong anchoring cell;
(b) effective λE of the collective excitation-induced standing wave in the weak anchoring cell.
( )
a( )
bFig. 2-4-6 (a) The structural formula of the LCP used in our experiment；(b) the morphological change of the LCP in the photopolymerization process.
The LCP was deposited on the top of the LPUV-defined photo-alignment layer of the cell. After illuminated by UV light, the polymerizable mesogenic groups in the photo-alignment layer were crosslinked to yield a small degree of uniaxial alignment.
This effect of inducing macroscopic alignment of LCP followed the photopolymerization process, improves the aligning quality of LC molecules in a LC
device [22, 23, 24]. The LC molecules contacting with the LCP surfaces thus possessed a higher order of orientation, and the corresponding orientation fluctuation mode was purer, which was supported by the observation that higher value of stretching parameter s was obtained for the photoalignment cell with composite layers of RN1349 and LCP.
To evaluate the possibility of our data in fact resulting from probing into the singularities or defects in the cell, we measured 50 more positions on each cell. The total experimental results are summarized in the following two histograms.
( )
a( )
bFig. 2-4-7 (a) Distribution of correlation times of the three cells with different surface treatments. 50 points were probed for each cell. The abscissa is correlation
time and the ordinate is its corresponding population; (b) distribution of stretching parameters of the three cells with different surface treatments. 50 points were probed for each cell. The abscissa is stretching parameter and the ordinate is its corresponding population.
From Fig. 2-4-7 (a), we can see that the mechanical rubbing cell does have smaller correlation times than those of photoalignment cells, this is in agreement with the fact that mechanical rubbing produces stronger anchoring strength than that produced by photoaligning method. We can deduce that the photoalignment cells have similar anchoring strength no matter whether LCP is deposited or not. However, from Fig.
2-4-7 (b), we find that LCP does play a role in improving the alignment order of LC molecules in the cell. By adding LCP layer, the stretching parameter s was improved to the level as that reached by the mechanical rubbing method.