{'fraction_non_alphanumeric': 0.015151515151515152, 'fraction_numerical': 0.0, 'mean_word_length': 4.9105691056910565, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Orientational Order of Surface-Aligned Nematic Liquid Crystals

The orientational order parameter of a uniformly aligned nematic liquid crystal bounded by two parallel substrates, with the same boundary conditions, is investigated by using the Maier-Saupe theory. It is shown that the orientational order parameter S varies along the normal to the boundary plane and takes the extremum value Se at the center of the cell, when the orientational order parameter Sb, at the boundary, is different from that of a free nematic liquid crystal So. It is also shown that Se converges to So exponentially as the cell thickness increases and S can be replaced by So in almost all regions, except the region extremely near the boundary.